A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

Question

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

Philoid · Accepted Answer

Given: let E₁ be the event of time consumed by machine A, E₂ be the event of time consumed by machine B and E₃ be the event of time consumed by machine C. Let X be the event of producing defective items.

Then

And

As we a headed coin has head on both sides so it will shows head.

Also P(X|E₁) = P (defective item produced by A)

And P(X|E₂) = P (defective item produced by B)

And P(X|E₃) = P (defective item produced by C)

Now the probability that item produced by machine A, being given that defective item is produced, is P(E₁|A).

By using bayes’ theorem, we have: